
The solution to this problem is obtained by using the
Karush-Kuhn-Tucker conditions [1]} and has a closed-form expression. It can be shown that it satisfies
\({\bar{M}\dot{\bar{v}} = \alpha - \mathcal {R}_{\bar{\mathcal {G}}}^\top ( \mathcal {R}_{\bar{\mathcal {G}}} \bar{M}^{-1} \mathcal {R}_{\bar{\mathcal {G}}}^\top )^\dagger (\dot{\mathcal {R}}_{\bar{\mathcal {G}}} \bar{v} + \mathcal {R}_{\bar{\mathcal {G}}} \alpha ),}\) 
